2019021201070920190211202142project_31.txt
Financial analysis – annuities, perpetuities, stock options
Please solve the attached problems. Show all work
Problem 1: Betty deposits an amount now and withdraws another amount after 9
months. 2 years after the initial deposit her account balance is $7,096.529. Bob
deposits twice what Betty did, now and withdraws after 15 months 300% of what
she withdrew. 2 years after his initial deposit his account balance is
$12,728.614.
If rates are 8% per annum effective then algebraically determine how much
Betty deposited and withdrew.
Problem 2: Betty deposits $5,000 now and deposits $3,000 after 1 year and
deposits $2,000 after 2 years. 3 years after the initial deposit her account
balance is $12,713.74.
Bob deposits $8,000 now and withdraws $2,500 after 1 year and deposits
$1,000 after 2 years. 3 years after his initial deposit his account balance is
$8,895.17.
Bertha deposits $6,000 now and withdraws $1,500 after 1 year and withdraws
$3,000 after 2 years. 3 years after her initial deposit her account balance is
$2,815.89.
If the continuous rates per annum are for the first year, for the second
year, and for the third year then algebraically find these three unknown rates.
Your final answers should be correct to 2 places after the decimal point.
Problem 3
An S&L pays 5% per annum compounded quarterly. Bert and Bertha are
now 50 years old. They will deposit $200 per quarter at the end of each
quarter until they are 65 years old.
a.
How much is in their retirement account at the end of this period i.e. at
65?
b.
3 months after their last deposit they start withdrawing equal amounts
each quarter until they are 80 i.e. for the next 15 years Find the size of the
withdrawals.
c.
How much cash did they deposit? How much cash did they withdraw? What was
the total interest?
Problem 4: An estate worth $3,500,000 and earning 24% per annum compounded
monthly makes equal payments of $75,000 at the end of each month to Betty and
Bob.
a.
Algebraically determine how many payments they will receive.
b.
Algebraically determine the amount of the last payment that will settle
the estate.
Problem 5: Betty and Bob borrow $850,000 at 12% per annum compounded monthly for
a 20 year (fixed rate) mortgage.
a.
What is their monthly payment?
b.
How much interest will they pay over the 20 years?
c.
After 10 years how much equity will they have in their property, i.e. how
much principal will they have paid?
d.
What will be the principal and interest components of the 120th payment?
The final answers of your algebraic work should be correct to 2 places after the
decimal point.
Problem 6: An antique automobile is depreciating, i.e. losing value i.e. going
down in price at a rate of 7% per annum compounded annually. Betty and Bob have
an account, which earns interest at a rate of 12% per annum continuously
compounded. They originally had $9,000 in the account and withdrew $2000 after
the second year and $2,500 after the third year. They had enough money (exactly)
to buy the automobile after 6 years. Algebraically find the original value of
the automobile. Your final answer should be correct to 2 places after the
decimal point.
Problem 7: Betty and Bob have an account with $0 in it. Interest rates are 12%
��per annum continuously compounded and they may borrow or loan at this rate. XYZ
�stock is $60 per share and they may buy or sell at this price. XYZ has a $0.50
(50 cent) dividend in 3, 6, and 9 months from now, which is allowed to earn
interest once it has been paid. A 10-month forward contract with a forward price
of $65.5 is available and they may go long or short it.
Betty and Bob wish to make money without risk. Advise them; that is tell
them how much to borrow or loan, buy or sell, go long or short to achieve a
risk-less profit after 10 months. How much profit do they make?
Be sure to algebraically explain all of your work. Your text in Section 27
should be helpful.
Problem 8: Betty and Bob are long 200 shares of XYZ @$42 and short 4 October 45
calls @$3 and long 1 October 40 put @$4. Analyze the algebraic value, W, and
profit and loss, Y, at expiration. Be sure to include formulae for W and Y. Be
sure to include a table analysis. Be sure to draw the graph of Y versus X, the
stock price at expiration. Algebraically determine the break-even points.
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